Since the pioneering work of Wonham [1]}, stochastic LQ problem has been extensively studied by numerous researchers. For instance, Bismut [2]} was the first one that studied stochastic LQ problems with random coefficients. But he could not solve the related stochastic Riccati equation (SRE) in general. Tang [3]} proved the existence and uniqueness of the SRE and solved the general stochastic LQ problem with uniformly positive control weighting matrix. Chen, Li and Zhou [4]} studied the indefinite stochastic LQ problem which is different obviously from its deterministic counterpart. Kohlmann and Zhou [5]} established the relationship between stochastic LQ problems and backward stochastic differential equations (BSDEs). Hu and Zhou [6]} solved the stochastic LQ problem with cone control constraint using Tanaka's formula. Please refer to Chapter 6 in Yong and Zhou [7]} for a systematic accounts on this subject.
